Would Carmelo Anthony have put the Tom Thibodeau-coached Bulls over the top?

Technically, Carmelo Anthony remains on the Bulls roster. Look for his name listed in the “inactives” if you’re suspicious or just want to let the mind wander.

Anthony, acquired in a cash deal from the Rockets, won’t report to the Bulls. He’ll eventually be traded or, most likely, waived.

But while he’s here, or not really here but on the roster, it’s easy to hark back to 2014. That’s when the Bulls coveted Anthony as the missing piece to a title team. That’s when Anthony, then-coach Tom Thibodeau and general manager Gar Forman donned construction hard hats to visit the not-yet-completed Advocate Center, a precious sight indeed.

It’s when Jim Boeheim, Anthony’s college coach at Syracuse, publicly said his former player should’ve signed with the Bulls instead of re-signing with the Knicks.

Indeed, James’ stunning decision to leave the Heat to return to his home-state team began a string of four straight NBA Finals appearances for the Cavaliers. Continuing his role dating to his time with the Heat when he foiled the Bulls as they led the NBA in regular-season victories, James stood as the biggest obstacle.

Anthony averaged 24.2 points in 2014-15, almost matching his career scoring average of 24 points. But he played in just 40 games before undergoing surgery in February 2015 for what the Knicks called “left knee patella tendon debridement and repair.”

Anthony proved more durable the next three seasons, playing in 72, 74 and 78 games. The Bulls would’ve signed him to a four-year deal. They were trying to keep Taj Gibson, which would have required Anthony to sign for roughly $50 million — and one season — less than his deal with the Knicks.

Trading Gibson would’ve cleared more cap space to lessen Anthony’s financial haircut. But Gibson played a big role in Anthony’s visit to Chicago, and multiple outlets, including the Tribune, reported at the time Anthony wanted Gibson to remain on the roster.

Had Anthony chosen the Bulls, he would’ve started alongside Derrick Rose, Gibson, Joakim Noah and Jimmy Butler. But not that Butler.

Phil Velasquez/Chicago Tribune

Bulls guard Derrick Rose leaves the United Center on July 1, 2014, after meeting with Carmelo Anthony.

Bulls guard Derrick Rose leaves the United Center on July 1, 2014, after meeting with Carmelo Anthony. (Phil Velasquez/Chicago Tribune)

Coming off his third season and first as full-time starter, Butler averaged 13.1 points but shot just 39.7 percent and 28.3 percent from 3-point range in 2013-14. Without Anthony, Butler took his first step toward stardom in 2014-15, winning the NBA Most Improved Player award by averaging 20 points and earning second team All-Defense honors.

Butler dramatically improved his shooting percentages that season but, with Anthony in the fold, would’ve averaged fewer than his 14 attempts per game. There even were some whispers the Bulls would have tried to move Butler, but Mike Dunleavy would have been a more likely trade option.

Rose played in 51 games in 2014-15. He averaged 17.7 points on 40.5 percent shooting, including an anemic 28 percent from 3-point range. Some league observers feel Rose and Anthony might have struggled to find chemistry, but Thibodeau never did.

“He probably doesn’t get the credit for being the passer and playmaker that he is,” Thibodeau said of Anthony before a Bulls-Knicks matchup that season. “The people with USA Basketball said that’s the role he played for that team.”

Indeed, Anthony drew widespread praise for his longtime commitment to USA Basketball. He’s the all-time leading scorer and rebounder but often deferred to other scorers such as James and Dwyane Wade while playing on three Olympic gold-medal-winning teams.

Phil Velasquez/Chicago Tribune

Bulls player Taj Gibson arrives at the United Center to meet with Carmelo Anthony on July 1, 2014.

Bulls player Taj Gibson arrives at the United Center to meet with Carmelo Anthony on July 1, 2014. (Phil Velasquez/Chicago Tribune)

Coincidentally, James’ Cavaliers eliminated the Bulls from the second round of the 2015 playoffs. Assuming Anthony had signed with the Bulls and stayed healthy, the matchups in that series would’ve featured Rose against Kyrie Irving, Butler against James, Anthony against Iman Shumpert, Gibson against Tristan Thompson and Noah guarding Timofey Mozgov.

When Anthony chose to re-sign with the Knicks, the Bulls quickly moved to contingency plans. They signed Pau Gasol, Kirk Hinrich, E’Twaun Moore and Aaron Brooks in free agency and completed Nikola Mirotic’s buyout from Real Madrid to finally bring over their 2011 draft-day acquisition.

By using the amnesty provision on Carlos Boozer, which the Bulls did that offseason, they would’ve been able to add some pieces along with Anthony. It’s just unknown which of the above reserves they would have been.

In fact, it’s far easier to speculate about what wouldn’t have happened had Anthony signed with the Bulls than what would have transpired.

Gasol wouldn’t have represented the Bulls in back-to-back All-Star Games. Butler wouldn’t have won Most Improved Player and signed a $95 million deal in free agency. Rose almost certainly wouldn’t have been traded to the Knicks in June 2016. The Three Alphas — shoutout to Rajon Rondo — wouldn’t have been a thing.

Would Thibodeau still be coaching? He had the closest working relationship with Anthony of anyone in the organization. Thibodeau and Anthony shared an agent. And Thibodeau’s association with USA Basketball as an assistant coach began in 2013.

Who knows what the shared USA Basketball connections of Thibodeau and Anthony, not to mention Anthony’s status in the “Banana Boat” foursome of him, Wade, James and Chris Paul, might’ve meant for future Bulls transactions?

Soon, Anthony will be another Bulls transaction, either traded or waived. Until then, he’ll be listed as inactive Sunday when the Bulls face — you guessed it — the Cavaliers, a rivalry that still might be raging had Anthony signed on the dotted line in 2014.